A high order projection method for nonlinear two point boundary value problems

1972 ◽  
Vol 20 (4) ◽  
pp. 257-270 ◽  
Author(s):  
Thomas R. Lucas ◽  
George W. Reddien
Keyword(s):  
Boundary Value Problems ◽  
Projection Method ◽  
Boundary Value ◽  
High Order ◽  
Point Boundary

scholarly journals Variable Mesh Size Exponential Finite Difference Method for the Numerical Solutions of Two Point Boundary Value Problems

2015 ◽  
Vol 34 (2) ◽  
pp. 9-27 ◽  
Author(s):  
Pramod K. Pandey ◽  
B. D. Pandey
Keyword(s):  
Finite Difference ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Mesh Size ◽  
High Order ◽  
Uniform Mesh ◽  
Point Boundary ◽  
Order Of Accuracy ◽  
Variable Mesh

In this article, we presented a non-uniform mesh size high order exponential finite difference scheme for the numerical solutions of two point boundary value problems with  Dirichlet's boundary conditions. Under appropriate conditions, we have discussed the local truncation error and the convergence of the proposed method. Numerical experiments have been carried out to demonstrate the use and high order computational efficiency of the present method in several model problems. Numerical results showed that the proposed method is accurate and convergent. The order of accuracy is at least cubic which is in good agreement with the theoretically established order of the method.

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